Take LSUN (bedroom) [1]} with \(256\times 256\)  resolution for a demonstration. Suppose we want to accelerate the NCSN++ [2]} up to \(5\times \)  (400 iterations). Direct acceleration leads to severe deterioration of the outputs as shown in Figure 3 of the main paper.
For quantization, we estimate the frequency statistics (Figure REF (left)) of the images generated by NSCN++ without acceleration as:
\(\phi _{p^\ast }(h,w) = \frac{1}{C}\sum _{c=1}^C\mathbb {E}_{\mathbf {x}\sim p^\ast (\mathbf {x})}\left[ D[\mathbf {x}]\odot D[\mathbf {x}] \right](h,w,c),1\le h \le H, 1\le w \le W,\) 
